LAMMP 4.2.0
Lamina High-Precision Arithmetic Library
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结构体 | 宏定义 | 类型定义 | 函数
longlong.h 文件参考
#include <stdint.h>
+ longlong.h 的引用(Include)关系图:
+ 此图展示该文件直接或间接的被哪些文件引用了:

浏览源代码.

结构体

struct  _udiv64_t
 

宏定义

#define _ADD_MARKER   0x40
 
#define _add_ssaaaa(sh, sl, ah, al, bh, bl)
 
#define _sub_ddmmss(sh, sl, ah, al, bh, bl)
 
#define _u128add(r, x, y)
 
#define _u128add64(r, x, _i64)
 
#define _u128cmp(x, y)   ((x)[1] < (y)[1] || ((x)[1] == (y)[1] && (x)[0] < (y)[0]))
 
#define _u128high(x)   (*((x) + 1))
 
#define _u128low(x)   (*(x))
 
#define _u128lshl(x, y, n)
 
#define _u128lshr(x, y, n)
 
#define _u128mul(r, x, y)   _umul64to128_((x), (y), (r), (((r) + 1)))
 
#define _u128sub(r, x, y)
 
#define _u128sub64(r, x, _i64)
 
#define _u192add(i192, j192)
 
#define _u192sub(i192, j192)
 
#define _U64_SHIFT_MASK   0x3F
 from https://libdivide.com/
 
#define _udiv32by32_q_preinv(q, n0, dinv)
 
#define _udiv_qr_3by2(q, r1, r0, n2, n1, n0, d1, d0, dinv)
 
#define _udiv_qrnnd_preinv(q, r, nh, nl, d, di)
 
#define clz_shl_u32(r, x, cnt)
 
#define clz_shl_u64(r, x, cnt)
 
#define ctz_shr_u32(r, x, cnt)
 
#define ctz_shr_u64(r, x, cnt)
 Copyright (C) 2026 HJimmyK(Jericho Knox)
 

类型定义

typedef struct _udiv64_t _udiv64_t
 
typedef uint64_t u128[2]
 
typedef uint64_t u192[3]
 

函数

static uint64_t _udiv128by64to64_ (uint64_t numhi, uint64_t numlo, uint64_t den, uint64_t *r)
 
static _udiv64_t _udiv64_gen (uint64_t d)
 
static _udiv64_t _udiv64_gen_internal_ (uint64_t d, int branchfree)
 
static uint64_t _udiv64by64_q_preinv (uint64_t numer, const _udiv64_t *denom)
 
static void _umul128to128_ (uint64_t a_high, uint64_t a_low, uint64_t b_high, uint64_t b_low, uint64_t rr[2])
 
static void _umul128to256_ (uint64_t a_high, uint64_t a_low, uint64_t b_high, uint64_t b_low, uint64_t rr[4])
 
static void _umul64to128_ (uint64_t a, uint64_t b, uint64_t *low, uint64_t *high)
 
static uint64_t _umul64to64hi_ (uint64_t a, uint64_t b)
 

结构体说明

◆ _udiv64_t

struct _udiv64_t

在文件 longlong.h 第 471 行定义.

+ _udiv64_t 的协作图:
成员变量
uint64_t magic
uint8_t more

宏定义说明

◆ _ADD_MARKER

#define _ADD_MARKER   0x40

在文件 longlong.h 第 469 行定义.

◆ _add_ssaaaa

#define _add_ssaaaa (   sh,
  sl,
  ah,
  al,
  bh,
  bl 
)
值:
do { \
uint64_t _x_; \
_x_ = (al) + (bl); \
(sh) = (ah) + (bh) + (_x_ < (al)); \
(sl) = _x_; \
} while (0)
n
#define n

在文件 longlong.h 第 399 行定义.

400 { \
401 uint64_t _x_; \
402 _x_ = (al) + (bl); \
403 (sh) = (ah) + (bh) + (_x_ < (al)); \
404 (sl) = _x_; \
405 } while (0)

◆ _sub_ddmmss

#define _sub_ddmmss (   sh,
  sl,
  ah,
  al,
  bh,
  bl 
)
值:
do { \
uint64_t _x_; \
_x_ = (al) - (bl); \
(sh) = (ah) - (bh) - ((al) < (bl)); \
(sl) = _x_; \
} while (0)

在文件 longlong.h 第 407 行定义.

408 { \
409 uint64_t _x_; \
410 _x_ = (al) - (bl); \
411 (sh) = (ah) - (bh) - ((al) < (bl)); \
412 (sl) = _x_; \
413 } while (0)

◆ _u128add

#define _u128add (   r,
  x,
  y 
)
值:
do { \
(*(r)) = *(x) + *(y); \
(*((r) + 1)) = (*((x) + 1)) + (*((y) + 1)) + ((*(r)) < (*(y)) ? 1 : 0); \
} while (0)

在文件 longlong.h 第 346 行定义.

347 { \
348 (*(r)) = *(x) + *(y); \
349 (*((r) + 1)) = (*((x) + 1)) + (*((y) + 1)) + ((*(r)) < (*(y)) ? 1 : 0); \
350 } while (0)

◆ _u128add64

#define _u128add64 (   r,
  x,
  _i64 
)
值:
do { \
(*(r)) = *(x) + (_i64); \
(*((r) + 1)) = (*((x) + 1)) + (((*(r)) < (_i64)) ? 1 : 0); \
} while (0)

在文件 longlong.h 第 352 行定义.

353 { \
354 (*(r)) = *(x) + (_i64); \
355 (*((r) + 1)) = (*((x) + 1)) + (((*(r)) < (_i64)) ? 1 : 0); \
356 } while (0)

◆ _u128cmp

#define _u128cmp (   x,
  y 
)    ((x)[1] < (y)[1] || ((x)[1] == (y)[1] && (x)[0] < (y)[0]))

在文件 longlong.h 第 366 行定义.

◆ _u128high

#define _u128high (   x)    (*((x) + 1))

在文件 longlong.h 第 342 行定义.

◆ _u128low

#define _u128low (   x)    (*(x))

在文件 longlong.h 第 344 行定义.

◆ _u128lshl

#define _u128lshl (   x,
  y,
  n 
)
值:
do { \
(*((x) + 1)) = ((*(y)) >> (64 - (n))) | ((*((y) + 1)) << (n)); \
(*(x)) = (*(y)) << (n); \
} while (0)

在文件 longlong.h 第 330 行定义.

331 { \
332 (*((x) + 1)) = ((*(y)) >> (64 - (n))) | ((*((y) + 1)) << (n)); \
333 (*(x)) = (*(y)) << (n); \
334 } while (0)

◆ _u128lshr

#define _u128lshr (   x,
  y,
  n 
)
值:
do { \
(*(x)) = ((*(y)) >> (n)) | ((*((y) + 1)) << (64 - (n))); \
(*((x) + 1)) = (*((y) + 1)) >> (n); \
} while (0)

在文件 longlong.h 第 336 行定义.

337 { \
338 (*(x)) = ((*(y)) >> (n)) | ((*((y) + 1)) << (64 - (n))); \
339 (*((x) + 1)) = (*((y) + 1)) >> (n); \
340 } while (0)

◆ _u128mul

#define _u128mul (   r,
  x,
  y 
)    _umul64to128_((x), (y), (r), (((r) + 1)))

在文件 longlong.h 第 375 行定义.

◆ _u128sub

#define _u128sub (   r,
  x,
  y 
)
值:
do { \
uint64_t _c_ = (x)[0] < (y)[0]; \
(r)[0] = (x)[0] - (y)[0]; \
(r)[1] = (x)[1] - (y)[1] - _c_; \
} while (0)

在文件 longlong.h 第 368 行定义.

369 { \
370 uint64_t _c_ = (x)[0] < (y)[0]; \
371 (r)[0] = (x)[0] - (y)[0]; \
372 (r)[1] = (x)[1] - (y)[1] - _c_; \
373 } while (0)

◆ _u128sub64

#define _u128sub64 (   r,
  x,
  _i64 
)
值:
do { \
uint64_t _c_ = (x)[0] < (_i64); \
(r)[0] = (x)[0] - (_i64); \
(r)[1] = (x)[1] - _c_; \
} while (0)

在文件 longlong.h 第 358 行定义.

359 { \
360 uint64_t _c_ = (x)[0] < (_i64); \
361 (r)[0] = (x)[0] - (_i64); \
362 (r)[1] = (x)[1] - _c_; \
363 } while (0)

◆ _u192add

#define _u192add (   i192,
  j192 
)
值:
do { \
(i192)[0] += (j192)[0]; \
uint64_t _c_ = ((i192)[0] < (j192)[0]) ? 1 : 0; \
(i192)[1] += _c_; \
_c_ = ((i192)[1] < _c_) ? 1 : 0; \
(i192)[1] += (j192)[1]; \
_c_ += ((i192)[1] < (j192)[1]) ? 1 : 0; \
(i192)[2] += _c_ + (j192)[2]; \
} while (0)

在文件 longlong.h 第 377 行定义.

378 { \
379 (i192)[0] += (j192)[0]; \
380 uint64_t _c_ = ((i192)[0] < (j192)[0]) ? 1 : 0; \
381 (i192)[1] += _c_; \
382 _c_ = ((i192)[1] < _c_) ? 1 : 0; \
383 (i192)[1] += (j192)[1]; \
384 _c_ += ((i192)[1] < (j192)[1]) ? 1 : 0; \
385 (i192)[2] += _c_ + (j192)[2]; \
386 } while (0)

◆ _u192sub

#define _u192sub (   i192,
  j192 
)
值:
do { \
uint64_t _b_ = ((i192)[0] < (j192)[0]) ? 1 : 0; \
(i192)[0] -= (j192)[0]; \
uint64_t _b1_ = ((i192)[1] < (j192)[1]) ? 1 : 0; \
(i192)[1] -= (j192)[1]; \
_b1_ += ((i192)[1] < _b_) ? 1 : 0; \
(i192)[1] -= _b_; \
(i192)[2] = (i192)[2] - ((j192)[2] + _b1_); \
} while (0)

在文件 longlong.h 第 388 行定义.

389 { \
390 uint64_t _b_ = ((i192)[0] < (j192)[0]) ? 1 : 0; \
391 (i192)[0] -= (j192)[0]; \
392 uint64_t _b1_ = ((i192)[1] < (j192)[1]) ? 1 : 0; \
393 (i192)[1] -= (j192)[1]; \
394 _b1_ += ((i192)[1] < _b_) ? 1 : 0; \
395 (i192)[1] -= _b_; \
396 (i192)[2] = (i192)[2] - ((j192)[2] + _b1_); \
397 } while (0)

◆ _U64_SHIFT_MASK

#define _U64_SHIFT_MASK   0x3F

from https://libdivide.com/

在文件 longlong.h 第 468 行定义.

◆ _udiv32by32_q_preinv

#define _udiv32by32_q_preinv (   q,
  n0,
  dinv 
)
值:
do { \
uint64_t _hi_, _lo_; \
_umul64to128_((n0), (dinv), &_lo_, &_hi_); \
(q) = _hi_; \
} while (0)

在文件 longlong.h 第 457 行定义.

458 { \
459 uint64_t _hi_, _lo_; \
460 _umul64to128_((n0), (dinv), &_lo_, &_hi_); \
461 (q) = _hi_; \
462 } while (0)

◆ _udiv_qr_3by2

#define _udiv_qr_3by2 (   q,
  r1,
  r0,
  n2,
  n1,
  n0,
  d1,
  d0,
  dinv 
)
值:
do { \
mp_limb_t _q0_, _t1_, _t0_, _mask_; \
_umul64to128_((n2), (dinv), &_q0_, &(q)); \
_add_ssaaaa((q), _q0_, (q), _q0_, (n2), (n1)); \
/* Compute the two most significant limbs of n - q'd */ \
(r1) = (n1) - (d1) * (q); \
_sub_ddmmss((r1), (r0), (r1), (n0), (d1), (d0)); \
_umul64to128_((d0), (q), &_t0_, &_t1_); \
_sub_ddmmss((r1), (r0), (r1), (r0), _t1_, _t0_); \
(q)++; \
/* Conditionally adjust q and the remainders */ \
_mask_ = -(uint64_t)((r1) >= _q0_); \
(q) += _mask_; \
_add_ssaaaa((r1), (r0), (r1), (r0), _mask_ & (d1), _mask_ & (d0)); \
if ((r1) >= (d1)) { \
if ((r1) > (d1) || (r0) >= (d0)) { \
(q)++; \
_sub_ddmmss((r1), (r0), (r1), (r0), (d1), (d0)); \
} \
} \
} while (0)
mp_limb_t
uint64_t mp_limb_t
Definition lmmp.h:76
r1
#define r1
r0
#define r0

在文件 longlong.h 第 432 行定义.

433 { \
434 mp_limb_t _q0_, _t1_, _t0_, _mask_; \
435 _umul64to128_((n2), (dinv), &_q0_, &(q)); \
436 _add_ssaaaa((q), _q0_, (q), _q0_, (n2), (n1)); \
437 /* Compute the two most significant limbs of n - q'd */ \
438 (r1) = (n1) - (d1) * (q); \
439 _sub_ddmmss((r1), (r0), (r1), (n0), (d1), (d0)); \
440 _umul64to128_((d0), (q), &_t0_, &_t1_); \
441 _sub_ddmmss((r1), (r0), (r1), (r0), _t1_, _t0_); \
442 (q)++; \
443 /* Conditionally adjust q and the remainders */ \
444 _mask_ = -(uint64_t)((r1) >= _q0_); \
445 (q) += _mask_; \
446 _add_ssaaaa((r1), (r0), (r1), (r0), _mask_ & (d1), _mask_ & (d0)); \
447 if ((r1) >= (d1)) { \
448 if ((r1) > (d1) || (r0) >= (d0)) { \
449 (q)++; \
450 _sub_ddmmss((r1), (r0), (r1), (r0), (d1), (d0)); \
451 } \
452 } \
453 } while (0)

◆ _udiv_qrnnd_preinv

#define _udiv_qrnnd_preinv (   q,
  r,
  nh,
  nl,
  d,
  di 
)
值:
do { \
uint64_t _qh_, _ql_, _r_, _mask_; \
_umul64to128_((nh), (di), &_ql_, &_qh_); \
_add_ssaaaa(_qh_, _ql_, _qh_, _ql_, (nh) + 1, (nl)); \
_r_ = (nl) - _qh_ * (d); \
_mask_ = -(mp_limb_t)(_r_ > _ql_); \
_qh_ += _mask_; \
_r_ += _mask_ & (d); \
if (_r_ >= (d)) { \
_r_ -= (d); \
_qh_++; \
} \
(r) = _r_; \
(q) = _qh_; \
} while (0)

在文件 longlong.h 第 415 行定义.

416 { \
417 uint64_t _qh_, _ql_, _r_, _mask_; \
418 _umul64to128_((nh), (di), &_ql_, &_qh_); \
419 _add_ssaaaa(_qh_, _ql_, _qh_, _ql_, (nh) + 1, (nl)); \
420 _r_ = (nl) - _qh_ * (d); \
421 _mask_ = -(mp_limb_t)(_r_ > _ql_); \
422 _qh_ += _mask_; \
423 _r_ += _mask_ & (d); \
424 if (_r_ >= (d)) { \
425 _r_ -= (d); \
426 _qh_++; \
427 } \
428 (r) = _r_; \
429 (q) = _qh_; \
430 } while (0)

◆ clz_shl_u32

#define clz_shl_u32 (   r,
  x,
  cnt 
)
值:
do { \
uint32_t _x_ = (x); \
int _c_ = 0; \
while ((_x_ & 0x80000000U) == 0) { \
_c_++; \
_x_ <<= 1; \
} \
(cnt) = _c_; \
(r) = _x_; \
} while (0)

在文件 longlong.h 第 161 行定义.

162 { \
163 uint32_t _x_ = (x); \
164 int _c_ = 0; \
165 while ((_x_ & 0x80000000U) == 0) { \
166 _c_++; \
167 _x_ <<= 1; \
168 } \
169 (cnt) = _c_; \
170 (r) = _x_; \
171 } while (0)

◆ clz_shl_u64

#define clz_shl_u64 (   r,
  x,
  cnt 
)
值:
do { \
uint64_t _x_ = (x); \
int _c_ = 0; \
while ((_x_ & 0x8000000000000000ULL) == 0) { \
_c_++; \
_x_ <<= 1; \
} \
(cnt) = _c_; \
(r) = _x_; \
} while (0)

在文件 longlong.h 第 88 行定义.

89 { \
90 uint64_t _x_ = (x); \
91 int _c_ = 0; \
92 while ((_x_ & 0x8000000000000000ULL) == 0) { \
93 _c_++; \
94 _x_ <<= 1; \
95 } \
96 (cnt) = _c_; \
97 (r) = _x_; \
98 } while (0)

◆ ctz_shr_u32

#define ctz_shr_u32 (   r,
  x,
  cnt 
)
值:
do { \
uint32_t _x_ = (x); \
int _i_ = 0; \
while ((_x_ & 1U) == 0) { \
_i_++; \
_x_ >>= 1; \
} \
cnt = _i_; \
(r) = _x_; \
} while (0)

在文件 longlong.h 第 147 行定义.

148 { \
149 uint32_t _x_ = (x); \
150 int _i_ = 0; \
151 while ((_x_ & 1U) == 0) { \
152 _i_++; \
153 _x_ >>= 1; \
154 } \
155 cnt = _i_; \
156 (r) = _x_; \
157 } while (0)

◆ ctz_shr_u64

#define ctz_shr_u64 (   r,
  x,
  cnt 
)
值:
do { \
uint64_t _x_ = (x); \
int _i_ = 0; \
while ((_x_ & 1) == 0) { \
_i_++; \
_x_ >>= 1; \
} \
cnt = _i_; \
(r) = _x_; \
} while (0)

Copyright (C) 2026 HJimmyK(Jericho Knox)

This file is part of LAMMP.

LAMMP is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License (LGPL) as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version.

This program is distributed WITHOUT ANY WARRANTY.

See https://www.gnu.org/licenses/.

在文件 longlong.h 第 74 行定义.

75 { \
76 uint64_t _x_ = (x); \
77 int _i_ = 0; \
78 while ((_x_ & 1) == 0) { \
79 _i_++; \
80 _x_ >>= 1; \
81 } \
82 cnt = _i_; \
83 (r) = _x_; \
84 } while (0)

类型定义说明

◆ _udiv64_t

typedef struct _udiv64_t _udiv64_t

◆ u128

typedef uint64_t u128[2]

在文件 longlong.h 第 327 行定义.

◆ u192

typedef uint64_t u192[3]

在文件 longlong.h 第 328 行定义.

函数说明

◆ _udiv128by64to64_()

static uint64_t _udiv128by64to64_ ( uint64_t  numhi,
uint64_t  numlo,
uint64_t  den,
uint64_t *  r 
)
inlinestatic

在文件 longlong.h 第 247 行定义.

247 {
248#if (defined(__GNUC__) || defined(__clang__)) && defined(USE_ASM)
249 uint64_t result;
250 __asm__("div %[v]" : "=a"(result), "=d"(*r) : [v] "r"(den), "a"(numlo), "d"(numhi));
251 return result;
252#elif defined(__GNUC__)
253 __uint128_t num = (__uint128_t)numhi << 64 | numlo;
254 uint64_t result = num / den;
255 *r = num % den;
256 return result;
257#elif defined(_MSC_VER) && (defined(_M_X64)) && (!defined(__clang__))
258 return _udiv128(numhi, numlo, den, r);
259#else
260 const uint64_t b = ((uint64_t)1 << 32);
261
262 uint32_t q1;
263 uint32_t q0;
264
265 uint64_t q;
266
267 int shift;
268
269 uint64_t den10 = den;
270 uint64_t num10 = numlo;
271
272 uint32_t den1;
273 uint32_t den0;
274 uint32_t num1;
275 uint32_t num0;
276
277 uint64_t rem;
278
279 uint64_t qhat;
280 uint64_t rhat;
281
282 uint64_t c1;
283 uint64_t c2;
284
285 if (numhi >= den) {
286 if (r)
287 *r = ~0ull;
288 return ~0ull;
289 }
290
291 clz_shl_u64(den, den, shift);
292 numhi <<= shift;
293 numhi |= (numlo >> (-shift & 63)) & (uint64_t)(-(int64_t)shift >> 63);
294 numlo <<= shift;
295
296 num1 = (uint32_t)(numlo >> 32);
297 num0 = (uint32_t)(numlo & 0xFFFFFFFFu);
298 den1 = (uint32_t)(den >> 32);
299 den0 = (uint32_t)(den & 0xFFFFFFFFu);
300
301 qhat = numhi / den1;
302 rhat = numhi % den1;
303 c1 = qhat * den0;
304 c2 = rhat * b + num1;
305 if (c1 > c2)
306 qhat -= (c1 - c2 > den) ? 2 : 1;
307 q1 = (uint32_t)qhat;
308
309 rem = numhi * b + num1 - q1 * den;
310
311 qhat = rem / den1;
312 rhat = rem % den1;
313 c1 = qhat * den0;
314 c2 = rhat * b + num0;
315 if (c1 > c2)
316 qhat -= (c1 - c2 > den) ? 2 : 1;
317 q0 = (uint32_t)qhat;
318
319 q = ((uint64_t)q1 << 32) | q0;
320
321 if (r)
322 *r = num10 - q * den10;
323 return q;
324#endif
325}
clz_shl_u64
#define clz_shl_u64(r, x, cnt)
Definition longlong.h:88
c1
#define c1

引用了 c1 , 以及 clz_shl_u64.

被这些函数引用 _udiv64_gen_internal_().

+ 这是这个函数的调用关系图:

◆ _udiv64_gen()

static _udiv64_t _udiv64_gen ( uint64_t  d)
inlinestatic

在文件 longlong.h 第 530 行定义.

530 {
531 _udiv64_t tmp = _udiv64_gen_internal_(d, 1);
532 _udiv64_t ret = {tmp.magic, (uint8_t)(tmp.more & _U64_SHIFT_MASK)};
533 return ret;
534}
_U64_SHIFT_MASK
#define _U64_SHIFT_MASK
from https://libdivide.com/
Definition longlong.h:468
_udiv64_gen_internal_
static _udiv64_t _udiv64_gen_internal_(uint64_t d, int branchfree)
Definition longlong.h:477
_udiv64_t::magic
uint64_t magic
Definition longlong.h:472
_udiv64_t
Definition longlong.h:471
tmp
#define tmp

引用了 _U64_SHIFT_MASK, _udiv64_gen_internal_(), _udiv64_t::magic , 以及 tmp.

被这些函数引用 lmmp_is_prime_uint_() , 以及 lmmp_powmod_uint_().

+ 函数调用图:
+ 这是这个函数的调用关系图:

◆ _udiv64_gen_internal_()

static _udiv64_t _udiv64_gen_internal_ ( uint64_t  d,
int  branchfree 
)
inlinestatic

在文件 longlong.h 第 477 行定义.

477 {
478 _udiv64_t result;
479 int shift;
480 uint64_t t;
481 clz_shl_u64(t, d, shift);
482 (void)t;
483 uint32_t floor_log_2_d = 63 - shift;
484
485 // Power of 2
486 if ((d & (d - 1)) == 0) {
487 // We need to subtract 1 from the shift value in case of an unsigned
488 // branchfree divider because there is a hardcoded right shift by 1
489 // in its division algorithm. Because of this we also need to add back
490 // 1 in its recovery algorithm.
491 result.magic = 0;
492 result.more = (uint8_t)(floor_log_2_d - (branchfree != 0));
493 } else {
494 uint64_t proposed_m, rem;
495 uint8_t more;
496 // (1 << (64 + floor_log_2_d)) / d
497 proposed_m = _udiv128by64to64_((uint64_t)1 << floor_log_2_d, 0, d, &rem);
498
499 const uint64_t e = d - rem;
500
501 // This power works if e < 2**floor_log_2_d.
502 if (!branchfree && e < ((uint64_t)1 << floor_log_2_d)) {
503 // This power works
504 more = (uint8_t)floor_log_2_d;
505 } else {
506 // We have to use the general 65-bit algorithm. We need to compute
507 // (2**power) / d. However, we already have (2**(power-1))/d and
508 // its remainder. By doubling both, and then correcting the
509 // remainder, we can compute the larger division.
510 // don't care about overflow here - in fact, we expect it
511 proposed_m += proposed_m;
512 const uint64_t twice_rem = rem + rem;
513 if (twice_rem >= d || twice_rem < rem)
514 proposed_m += 1;
515 more = (uint8_t)(floor_log_2_d | _ADD_MARKER);
516 }
517 result.magic = 1 + proposed_m;
518 result.more = more;
519 // result.more's shift should in general be ceil_log_2_d. But if we
520 // used the smaller power, we subtract one from the shift because we're
521 // using the smaller power. If we're using the larger power, we
522 // subtract one from the shift because it's taken care of by the add
523 // indicator. So floor_log_2_d happens to be correct in both cases,
524 // which is why we do it outside of the if statement.
525 }
526 return result;
527}
_ADD_MARKER
#define _ADD_MARKER
Definition longlong.h:469
_udiv128by64to64_
static uint64_t _udiv128by64to64_(uint64_t numhi, uint64_t numlo, uint64_t den, uint64_t *r)
Definition longlong.h:247
t
#define t

引用了 _ADD_MARKER, _udiv128by64to64_(), clz_shl_u64, _udiv64_t::magic, _udiv64_t::more , 以及 t.

被这些函数引用 _udiv64_gen().

+ 函数调用图:
+ 这是这个函数的调用关系图:

◆ _udiv64by64_q_preinv()

static uint64_t _udiv64by64_q_preinv ( uint64_t  numer,
const _udiv64_t *  denom 
)
inlinestatic

在文件 longlong.h 第 536 行定义.

536 {
537 uint64_t q = _umul64to64hi_(numer, denom->magic);
538 uint64_t t = ((numer - q) >> 1) + q;
539 return t >> denom->more;
540}
_umul64to64hi_
static uint64_t _umul64to64hi_(uint64_t a, uint64_t b)
Definition longlong.h:194

引用了 _umul64to64hi_(), _udiv64_t::magic, _udiv64_t::more , 以及 t.

被这些函数引用 lmmp_powmod_uint_(), miller_rabin_32(), trial_div13(), trial_div17(), trial_div19(), trial_div23(), trial_div29(), trial_div31(), trial_div37() , 以及 trial_div41().

+ 函数调用图:
+ 这是这个函数的调用关系图:

◆ _umul128to128_()

static void _umul128to128_ ( uint64_t  a_high,
uint64_t  a_low,
uint64_t  b_high,
uint64_t  b_low,
uint64_t  rr[2] 
)
inlinestatic

在文件 longlong.h 第 241 行定义.

241 {
242 _umul64to128_(a_low, b_low, rr, rr + 1);
243 rr[1] += a_low * b_high;
244 rr[1] += a_high * b_low;
245}
_umul64to128_
static void _umul64to128_(uint64_t a, uint64_t b, uint64_t *low, uint64_t *high)
Definition longlong.h:174

引用了 _umul64to128_().

被这些函数引用 lmmp_binvert_4_(), lmmp_binvert_unbalanced_2_() , 以及 lmmp_divexact_2_().

+ 函数调用图:
+ 这是这个函数的调用关系图:

◆ _umul128to256_()

static void _umul128to256_ ( uint64_t  a_high,
uint64_t  a_low,
uint64_t  b_high,
uint64_t  b_low,
uint64_t  rr[4] 
)
inlinestatic

在文件 longlong.h 第 212 行定义.

212 {
213 uint64_t p1_low, p1_high; // p1 = a_low × b_high
214 uint64_t p2_low, p2_high; // p2 = a_high × b_low
215 _umul64to128_(a_low, b_low, rr, rr + 1);
216 _umul64to128_(a_low, b_high, &p1_low, &p1_high);
217 _umul64to128_(a_high, b_low, &p2_low, &p2_high);
218 _umul64to128_(a_high, b_high, rr + 2, rr + 3);
219 /*
220 | res0 | res1 | res2 | res3 |
221 | p0l | p0h | | |
222 | p1l | p1h | |
223 | p2l | p2h | |
224 | | p3l | p3h |
225 */
226 rr[1] += p1_low;
227 uint64_t carry = (rr[1] < p1_low) ? 1 : 0;
228 rr[1] += p2_low;
229 carry += (rr[1] < p2_low) ? 1 : 0;
230
231 rr[2] += carry;
232 carry = (rr[2] < carry) ? 1 : 0;
233 rr[2] += p1_high;
234 carry += (rr[2] < p1_high) ? 1 : 0;
235 rr[2] += p2_high;
236 carry += (rr[2] < p2_high) ? 1 : 0;
237
238 rr[3] += carry;
239}

引用了 _umul64to128_().

被这些函数引用 lmmp_binvert_4_(), lmmp_binvert_unbalanced_2_() , 以及 lmmp_divexact_2_().

+ 函数调用图:
+ 这是这个函数的调用关系图:

◆ _umul64to128_()

static void _umul64to128_ ( uint64_t  a,
uint64_t  b,
uint64_t *  low,
uint64_t *  high 
)
inlinestatic

在文件 longlong.h 第 174 行定义.

174 {
175#if (defined(__GNUC__) || defined(__clang__))
176 __uint128_t prod = (__uint128_t)a * b;
177 *low = (uint64_t)prod;
178 *high = (uint64_t)(prod >> 64);
179#elif defined(_MSC_VER) && (defined(_M_X64) || defined(_M_ARM64))
180 *low = _umul128(a, b, high);
181#else
182 uint64_t ah = a >> 32, bh = b >> 32;
183 a = (uint32_t)a, b = (uint32_t)b;
184 uint64_t r0 = a * b, r1 = a * bh, r2 = ah * b, r3 = ah * bh;
185 r3 += (r1 >> 32) + (r2 >> 32);
186 r1 = (uint32_t)r1, r2 = (uint32_t)r2;
187 r1 += r2;
188 r1 += (r0 >> 32);
189 *high = r3 + (r1 >> 32);
190 *low = (r1 << 32) | (uint32_t)r0;
191#endif
192}
r2
#define r2
r3
#define r3

引用了 r0, r1, r2 , 以及 r3.

被这些函数引用 _umul128to128_(), _umul128to192_(), _umul128to256_(), lmmp_addmul_1_(), lmmp_binvert_2_(), lmmp_binvert_4_(), lmmp_binvert_unbalanced_1_(), lmmp_divexact_1_(), lmmp_inv_2_1_(), lmmp_mul_1_(), lmmp_mul_basecase_(), lmmp_mulmod_ulong_(), lmmp_sqr_basecase_(), lmmp_submul_1_(), pcg64_128_action(), umul128x64_tohi128() , 以及 umul192x128_tohi192().

+ 这是这个函数的调用关系图:

◆ _umul64to64hi_()

static uint64_t _umul64to64hi_ ( uint64_t  a,
uint64_t  b 
)
inlinestatic

在文件 longlong.h 第 194 行定义.

194 {
195#if (defined(__GNUC__) || defined(__clang__)) && defined(__SIZEOF_INT128__)
196 __uint128_t t = (__uint128_t)a * (__uint128_t)b;
197 return (uint64_t)(t >> 64);
198#elif defined(_MSC_VER) && (defined(_M_X64) || defined(_M_ARM64))
199 return __umulh(a, b);
200#else
201 uint64_t ah = a >> 32, bh = b >> 32;
202 a = (uint32_t)a, b = (uint32_t)b;
203 uint64_t r0 = a * b, r1 = a * bh, r2 = ah * b, r3 = ah * bh;
204 r3 += (r1 >> 32) + (r2 >> 32);
205 r1 = (uint32_t)r1, r2 = (uint32_t)r2;
206 r1 += r2;
207 r1 += (r0 >> 32);
208 return r3 + (r1 >> 32);
209#endif
210}

引用了 r0, r1, r2, r3 , 以及 t.

被这些函数引用 _udiv64by64_q_preinv().

+ 这是这个函数的调用关系图: